The fondamental thing here is that humans 40k years ago could live in the toundra because we can live in the toundra today, and they had a similar behaviour to ours. So they made clothes and fires for the cold, and weapons for hunting the local fauna, just like we do. And they avoided actually desolate areas because they could not live without food.

That's why the colonisation of colder areas happened at about the time of behavioural modernity. Before that, humans where anatomically modern (mostly identical to us) but did not have the cultural equipment to deal with difficult environments.